Power transmitting apparatus



Nv. 3, 1936. l R. G. MccuRDY 2,059,738

POWER TRANSMITTING APPARATUS Filed June 19, 1926 Tiql."

Patented Nov. 3, 1936 UNITED STATES ,PATENT OFFICE PowElt "PRANSMITTINGAPPARATUS Ralph Gordon MeCurdy, Englewood, N. J. Application June 19,192s, serial N0. 117,130 s claims. (c1. 172-246) An important limitationto the amount of power which may be transmitted over long transmissionlines byalternating voltages and currents, is the phase change whichoccurs 4between the two ends, caused by the series inductance and shuntcapacitance of the line. By phase change is meant the displacement inphase of the line voltage at opposite ends of the line or the phasedisplacement of line current at opposite ends of the line. In order totransmit power over the line in varying amounts, as determined by therequirements of the load, with denite voltages at the two ends,correcting means mustbe provided. In present practice, these correctingmeans consist of synchronous apparatus whose excitations may b e variedoverA a wide range and which may supply leading or lagging current tothe system as may be necessary to transmit the power required by theload.

By my invention I propose to connect stationf-v ary apparatus to theline, such apparatus having a phase change at the particular frequencyof voltage and current at which they power is being transmitted, whichopposes the phase change caused by the transmission line. By suitablyrelating the constants of the correcting apparatus-to thecharacteristics of the transmission line, the combination may be madevto have, at a particular frequency, the characteristics of amuchshorter transmission line, to function like a line having onlyresistance characteristics, or to behave as` though the line had seriescapacitance and shunt inductance instead oglseries inductance and shuntcapacitance.

Figure 1 is a diagram of a power transmitting system embodying'myinvention, Figure 2 is a diagram showing an alternative form ofvcorrecting apparatus, Figure 3 is a diagram showing a line and phasecorrecting means alternately disposed and Figure 4 is a diagram of athree-phase system, includingl the correcting apparatus of my invention.

As is well known in the art the characteristic impedance Zo, 'andpropagation constant, I, of a transmission line having seriesresistance, R, series inductance, L, shunt conductor G and shuntcapacitance, C, per mile is given -by the following relations:

(1) may be rewritten On the assumption that C42/MC2, ft2/w21?, andGR/u2LC are small compared to 1, which is justifiable in the types oftransmission line we are considering,

(2) may be rewritten,

Onthe same assumptions as those used above in simplifying (3),

On the same assumption as used in simplifying (10) It will be seen bycomparing Equations (l0) and (12) with Equations (5) and (7) that thetwo types of line will have equal characteristic impedances and wavelength constants per mile of equal magnitude and opposite sign when 1 wLC=w 1/L,=C, (13) L l (fea/t 1 and R Q ll l TL- wC)-R mC G L (15) from(13) `and (14) 1 1 wLf--Cl wC==Z (16) substituting (16) in (15) Vl l R+R=G +G (17) It will be understood of course that since R and R are bothsmall compared to aL, and G and G' small compared to wC, considerabledeparture from Equation (17) may be permitted without appreciablyaecting the equality of Zo and Zo' and and It is well known in the artthat when two lines of equal characteristic impedancesand differentpropagation constants are connected together the relations among thevoltages, currents, and powers at the two ends of the composite systemmay be determined by replacing the composite system by an equivalentuniform line with the same characteristic impedance and with a totalpropagation constant equal to the sum of the products of the propagationconstants per unit length of the individual sections of the compositesystem times their respective lengths.

When a, line of length D having series capacitance and shunt inductanceis connected to a transmission line of length D with series inductanceand shunt capacitance and their primary constants are related inaccordance with Equations (16) and (17), the attenuation constant of thecomposite system is the sum of the products of the attenuation constantsof the individual sections times their respective lengths, while thewave length constant of the composite system is the product of the wavelength constant of the real line times the difference in the lengths.Thus the total propagation constant is i=aD+aD+j/3(DD') (18) It is thuspossible to make the composite system to function at the given frequencylike a line of pure resistances by making D and D equal, like a line ofseries inductance and shunt capacitance of any desired length less thanD by making D' less than D or like a line of series capacitance andshunt inductance of any desired length by making D' greater than D.

As far as functioning at a single frequency ls concerned. it is wellknown in the art that a smooth line may be replaced by an equivalentartincial line having lumped constants. .This may be either a 1r or a Tstructure. If a 1r structure with two equal shunt admittances Ya at eachend and series impedance Za be chosen, these constants are related tothe constants of the smooth line by the following well known Iormulae:(See A. E. Kennelly, The Application of Hyperbolic Functions toElectrical Engineering Problems University of London Press 1912,formulae (77) and (78) page 33).

by well known formulae of hyperbolic trigonometry these Equations (21)and (22) may be rewritten It will be evident therefore that byproportioning Zu and Ya to the constants of the transmission line andthe desired value of D by the use of Equations (23) and (24) thecombination of the transmission line of the length Dand articial linemay be made to have the phase change of a transmission line oi a lengthD-D.

It Will be understood that this correcting apparatus may be connected ateither the sending or the receiving end of the transmission line or thatthe transmission line may be divided into a plurality of sections withcorrecting apparatus connected between the adjacent sections. When thecorrecting apparatus is placed at one or the other end o1' a section ofthe the apparatus may be said to be in tandem with the section of line.In order that the Wave length factor of the combination shall be equalto the wave length factor o1' a line of the length D-D. where D is thetotal length of the line, the summation of the equivalent lengths of thesections of correcting apparatus must equal D.

If desired, when a 1r artificial line is used as the phase correctingmeans the shunt branch adjacent to the load may be omitted. This isequivalent in its effect to connecting in parallel with the load anadmittance opposite in sign and equal in magnitude to the admittance ofthe omitted branch.

I will now disclose a number of examples of the application of myinvention it being understood that `the invention is defined in theappended claims:

Fig. 1 shows a diagram of a single-phase power transmission circuitcomprising a generator I, a step up transformer 2, a transmission line3, phase corrective apparatus I, consisting of a series branch 8comprising a transformer 9 associated with capacitance I0, andinductance shunts 1, step down transformer 5 and load 6.

transmission line,

Choosing D' as 2504 miles and letting the effective resistance of Zwbe 2per cent., the correcting apparatus has the following constants:

Za3.5j177.3 Ohms Shunt branches, 7 Ya24.7-j739 micromhos Attenuationconstant D' a' 0.014

Wave length constant D' 0.517

The combination of the transmission line and the correcting apparatushas the following characteristics:

Series branch, 8

Characteristic impedance 358-f1.8 Attenuation constant Da-l-D' a 0.066Wave length constant D-I- D i er losses of the system will need to besupplied which will be small compared to the power rating of thegenerator. With a load there will be a drop in voltage due to theresistance losses butthis drop will be very small compared to that whichwould occur on the line without the correcting means.

If D be taken as 275 miles-the corrective apparatus will have thefollowing constants.

Za 3.9j193.0 oh'ms Shunt branches, 7 Y a 28.8 -j816.0 micromhosAttenuation constant Da' 0.0162 Wave length constant D' 0.568

The combination of the transmission line and Series branch, 8

the phase correcting apparatus will have thel following characteristics:

Characteristic impedance 358 j l .8 v Attenuation constant Da+ Da 0.068Wave length constant D -l- D' 0.05 2

When the load 6 has a lagging power factor the eifect of the negativewavelength factor of this combination will be to counteract theresistance drop or attenuation factor and to permit the transmission ofa large amount of. power with substantially equal voltages on the highsides of transformers 2 and 5.

The lengths of uncorrected line chosen for the above examples are each afraction of a quarter wave length.

In Fig. 2 I show a line 3 and phase-correcting apparatus Il, thecorrecting apparatus comprising a shunt branch I2 and two Vseriesbranches I3.

In Fig. 3 I show a combination of a generator I, a section oftransmission line I4, correcting apparatus I5, a second section oftransmission line I4, a second section of correcting apparatus -I5, andload 6.

In Fig. 4 I show one way in which my invention may be applied to athree-phase power-transe mission circuit. This figure includes athreephase generator II,y step up transformers I1, with vtheir primariesin delta and their secondaries in star, extended transmission line I8,correcting apparatus I9, comprising six delta-connected shunt branches22 and series transformers 23' associated with three capacitances 24,star-delta connected step-down transformers 20 and load 2 I I claim:

1. In combination, a source of power, a step-up transformer, atransmission line, phase-correcting apparatus comprising Atwoshuntreactances and a series transformer, associated with a capacitance,a step-down transformer and a load, said phase-correcting-apparatushaving a characteristic impedance equalilto the characteristic impedanceof the transmission line and a wavelength constant opposite to thewave-length constant of the transmission line. A

2. In combination, a source of power, a transmission line, phasecorrecting apparatus consisting of lumped impedances connected in seriesand yshunt to the line, said correcting apparatus having acharacteristic impedance substantially equal to the characteristicimpedance of the transmission line` and wave length constant opposite insign to the wave length constant of the transmission line, a step-downtransformer and `a load. v

shunt to the line and a. capacity in series with the line, a step-downytransformer and a load,

said phase correcting apparatus having a characteristicimpedancesubstantially equal to the characteristic impedance of thetransmission line and a wave length constant opposite'in sign to thewave length constant of the transmission line.

4. In combination, a source of power, an extended transmission line, aload, and phase correcting apparatus forming an artificial line withlumped constants connected'in shunt and series with the transmissionline, said artificial line having a characteristic impedancesubstantially equal to that of the transmission line and saidarticialline having a wave length constant of opposite sign'to that ofthe transmission line.

5. In a system `of electrical wave transmission, a non-uniformwave-conductor consisting of a conductor having capacity reactancesources in series relation and inductive reactance sources in shuntrelation distributed at points along its length in such manner that theresulting wave conductor lsjequivalent, within proper limits, to itscorresponding uniform conductor but of re-. ducedeffective seriesreactance and of increased shunt reactance, substantially as described.

6. In combination' an extended power transmissionline with capactativereactance in series with the line and inductive reactance in shunt tothe line, said rcactances being proportioned to each other and to theconstants of the transmission line so that throughout changes in loadthev line voltage and current at one part of the combined system aresubstantially in phase respectively with the lineV voltage and currentat a distant part of the combined system.

'7. In a system of electrical wave transmission, a non-uniform waveconductor consisting of a uniform conductor having capacity reactancesources in series relation and inductivereactanc sources in shuntrelation, distributed at points conductor, a predetermined inductancereactance and capacity per unit length, the distance between theinterposed reaotanoes being adjusted in such a. Way as to equal afractional part of one quarter of the wave length which is to betransmitted.

8. In combination an extended power transmission line with capacitativereactance in series with the line and inductive reactance in shuntactance.

`lent within proper limits to a Atransmission line of substantiallyreduced effective series reactance and substantially increased eiectiveshunt re- RALPH G. MCCURDY.

